So this is like the left-sided closure of $A$; it contains all the points that $A$ 'converges to' from the left. We can define $rcl(A)$ similarly. I am wondering what the best way to think about these objects is. There seem like too many choices. In my particular situation, I am dealing with topologically unpleasant objects (uncountable unions of pw-disjoint Cantor Sets), so anything that is well suited to such applications is preferable.

To ask more of a question than a reference request, what can be said about infinite unions of Cantor sets, either countably or uncountable? Anything that falls out of the definition?

Thanks! I tagged some topics that seem most likely to contribute, but if anyone has other suggestions, then that would also be helpful.